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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{\sec\left(x\right)}\frac{d}{dx}\left(\sec\left(x\right)\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(ln(sec(x))). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x). The derivative of the linear function is equal to 1. Multiply the fraction and term.